Stability, L2-gain analysis and state-feedback H∞ control of linear systems with uncertain time-varying delays are considered in the case, where the nominal values of delays are constant and non-zero. A new construction of Lyapunov–Krasovskii functionals (LKFs) is introduced: to a nominal LKF, which is appropriate to the system with nominal delays, terms are added that correspond to the perturb...

In this brief, the problem of exponential dissipativity of discrete-time switched system with time-varying delays is proposed by using the average dwell time approach and multiple Lyapunov-Krasovskii functional (LKF).

Stability of linear systems with norm-bounded uncertainties and uncertain time-varying delays is considered. The delay is supposed to be bounded and fast varying (without any constraints on the delay derivative). Sufficient stability conditions are derived by direct Lyapunov method based on the complete Lyapunov–Krasovskii functional (LKF). A novel complete LKF construction is presented: the de...

An investigation of the input-to-state practical stability (ISpS) and integral (iISpS) nonlinear systems with time delays (NSWTDs) is presented in this paper. The ISpS iISpS are obtained by using a continuously differentiable Lyapunov–Krasovskii functional (LKF) within-definite derivative, which generalizes classical LKF positive definite derivative. As result, uniform asymptotic (UPAS) criteri...

This paper addresses the problem of stability analysis for a class of genetic regulatory networks (GRNs) with Markovian jumping parameters and time-varying delays. By constructing a novel Lyapunov-Krasovskii functional (LKF) and using an appropriate enlargement scheme, new stability criteria are proposed in terms of linear matrix inequalities, which can guarantee the mean square stability of Ma...

This paper presents a robust stability problem for linear uncertain discrete-time systems with interval timevarying delay and norm-bounded uncertainties. First, a necessary and sufficient stability condition is obtained by employing a well-known lifting method and switched system approach for nominal discrete-time delay systems. Both the stability method of checking the characteristic values in...

This paper focuses on the problem of finite-time boundedness and finite-time passivity of discrete-time T-S fuzzy neural networks with time-varying delays. A suitable Lyapunov--Krasovskii functional(LKF) is established to derive sufficient condition for finite-time passivity of discrete-time T-S fuzzy neural networks. The dynamical system is transformed into a T-S fuzzy model with uncertain par...

This paper deals with the problem of delay-dependent stability and the stabilization of Takagi-Sugeno (T-S) fuzzy systems with a time-varying delay while imposing positivity in closed-loop. The stabilization conditions are derived using the single Lyapunov-Krasovskii Functional (LKF) combining the introduction of free-single matrices. A memory feedback control is also used in case the delay mat...

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities LMIs . By free-weight matrices method, the usual res...

This paper is concerned with the robust stability of uncertain neutral-type Lur’e system with interval time-varying delays and sector-bounded nonlinearities. By use of augmented Lyapunov-Krasovskii functional (LKF) and delay-partitioning techniques, delay-dependent robust stability criteria are proposed in terms of linear matrix inequalities (LMIs) without using the general free-weighting matri...